Name: hydraulic jump in a rectangular channel
Uploaded: 2025-03-26T15:04:36.000Z
Duration: 1 min 16 s
Channel: JoVE

Water flows through a rectangular channel at 6 meters per second. When a gate at the end of the channel suddenly closes, a wave called a hydraulic jump travels upstream at 2 meters per second.&nbsp;In front of the jump, the wave's velocity combines the channel's initial flow, resulting in an effective upstream velocity of 8 meters per second. Behind the jump, the water flows at a speed of 2 meters per second.Since the flow rate remains constant, the downstream-to-upstream velocity ratio is 1:4, so the downstream depth is four times the upstream depth.To analyze the hydraulic jump, the Froude number, which relates flow inertia to gravity,&nbsp;is calculated as the upstream velocity divided by the square root of gravitational acceleration times the upstream depth.&nbsp;Using this, the upstream depth is determined as 0.652 meters. Multiplying by four yields a downstream depth of 2.61 meters.As a result, the depth ahead of the jump is 0.65 meters, and behind it, 2.61 meters.

hydraulic jump: problem solving

To analyze a hydraulic jump in a rectangular channel with a flow speed of 6 meters per second, follow these steps:<ol><li>Calculate Effective Upstream Velocity: When the downstream gate closes, a hydraulic jump forms, traveling upstream at 2 meters per second. This wave speed combines with the initial channel flow velocity, creating an effective upstream velocity.</li><li>Identify Flow Velocities Before and After the Hydraulic Jump: Upstream of the hydraulic jump, the effective flow velocity includes both the channel flow and wave speed. Downstream, the flow matches the wave speed, which is slower than the initial upstream velocity.</li><li>Establish Velocity Ratio for Depth Calculation: Because the flow rate remains constant, the ratio of downstream to upstream velocity impacts the depth of the water. In this example, the downstream depth is four times the upstream depth.</li><li>Calculate the Froude Number: The Froude number, which compares flow inertia to gravitational forces, is calculated using upstream flow characteristics. This number helps determine the upstream depth.</li><li>Determine Upstream Depth: Calculate the upstream depth from the channel bottom to the water surface using the upstream velocity and Froude number.</li><li>Calculate Downstream Depth: Since the downstream depth is four times the upstream depth, this value is calculated based on the upstream depth.</li><li>Summarize Depths Across the Hydraulic Jump: The results show that the water depth ahead of the hydraulic jump is significantly shallower than behind it, reflecting changes in depth due to flow conditions and wave behavior.</li></ol>These steps provide a clear method for analyzing the hydraulic jump, illustrating how flow characteristics affect water depth across the channel.

Hydraulic Jump: Problem Solving

To analyze a hydraulic jump in a rectangular channel with a flow speed of 6 meters per second, follow these steps:Calculate Effective Upstream ...

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JoVE Core

Civil Engineering

Unit 1

Open Channel Flow

KEY TERMS AND CONCEPTS

hydraulic jump in a rectangular channel

Hydraulic jump in a rectangular channel shows how flow speed and water depth change when a gate closes downstream. The jump travels upstream at 2 meters per second, so that wave speed is part of the calculation. The initial channel flow speed is 6 meters per second.

To find the water depths on each side of the jump, first calculate the effective upstream velocity. This combines the flow moving through the channel with the upstream-moving wave. Next, identify the flow velocities before and after the hydraulic jump. Upstream of the jump, the velocity includes both the channel flow and the wave speed. Downstream, the flow matches the wave speed, which is slower than the original upstream flow.

The flow rate stays constant, so the velocity ratio helps determine the depth ratio. In this example, the downstream depth is four times the upstream depth. The Froude number is then calculated from the upstream flow. The Froude number compares flow inertia with gravitational forces, and it helps determine the upstream depth.

After the upstream depth is found, the downstream depth can be calculated from the four-to-one depth ratio. The result shows shallow water ahead of the hydraulic jump and deeper water behind it. This pattern reflects how flow conditions and wave motion change water depth across the channel.

Hydraulic Jump in a Rectangular Channel

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key terms and concepts

Use flow speed, wave speed, and the Froude number to compare water depth before and after a hydraulic jump in a rectangular channel.

Hydraulic Jump in a Rectangular Channel | JoVE K12

JoVE Core Civil Engineering offers a foundational exploration of essential construction materials such as bricks, stones, steel, wood, and concrete, along with fluid mechanics topics like flow over immersed bodies, open channel flow, and dimensional modeling. It also covers key surveying concepts, including leveling, traverse adjustments, curve design, topographic mapping, and geospatial technologies (GPS & GIS). Science-in-action videos showcase laboratory research on materials, fluids, and surveying practices in real-world engineering systems.

civil engineering

Hydraulic Jump in a Rectangular Channel

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